LARGE TIME BEHAVIOR OF SOLUTION TO NONLINEAR DIRAC EQUATION IN 1+1 DIMENSIONS
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摘要
This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R~(1+1). It is shown that the solution will tend to travelling wave solution when time tends to infinity.
This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R~(1+1). It is shown that the solution will tend to travelling wave solution when time tends to infinity.
This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R~(1+1). It is shown that the solution will tend to travelling wave solution when time tends to infinity.
引文
[1]Beale J. Large-time behavior of the Broadwell model of a discrete velocity gas. Comm Math Phys, 1985,102(2):217-235
[2]Bournaveas N, Zouraris G E. Theory and numerical approximations for a nonlinear 1+1 Dirac system.ESAIM Math Model Num Analysis, 2012, 46(4):841-874
[3]Cacciafesta F. Global small solutions to the critical radial Dirac equation with potential. Nonlinear Analysis,2011, 74:6060-6073
[4]Candy T. Global existence for an L2 critical nonlinear Dirac equation in one dimension. Adv Differential Equations, 2011, 16(7/8):643-666
[5]Chen S X. Cauchy problem for semilinear hyperbolic equation of higher order with discontinuous initial data. Acta Math Sci, 1994, 14B(2):121-129
[6]Contreras A, Pelinovsky D, Shimabukuro Y. L2 orbital stability of Dirac solitons in the massive Thirring model. Comm Partial Differential Equations, 2016, 41(2):227-255
[7]Delgado V. Global solution of the Cauchy problem for the(classical)coupled Maxwell-Dirac and other nonlinear Dirac equations. Proc Amer Math Soc, 1978, 69(2):289-296
[8]Escobedo M, Vega L. A semilinear Dirac equation in H~s(R~3)for s> 1. SIAM J Math Anal, 1997, 28(2):338-362
[9]Gross D J, Neveu A. Dynamical symmetry breaking in asymptotically free field theories. Phys Rev D,1974,10:3235-3253
[10]Huh H. Global strong solution to the Thirring model in critical space. J Math Anal Appl, 2011, 381:513-520
[11]Huh H. Global solutions to Gross-Neveu equation. Lett Math Phys, 2013, 103(8):927-931
[12]Huh H, Moon B. Low regularity well-posedness for Gross-Neveu equations. Commun Pure Appl Anal, 2015,14(5):1903-1913
[13]Lax P. Functional Analysis. John Wiely Sons Inc, 2002
[14]Pelinovsky D. Survey on global existence in the nonlinear Dirac equations in one dimension//Ozawa T,Sugimoto M. Harmonic Analysis and Nonlinear Partial Differential Equations. RIMS Kokyuroku Bessatsu,2011:37-50
[15]Sasaki H. Small data scattering for the one-dimensional nonlinear Dirac equation with power nonlinearity.Comm Partial Differential Equations, 2015, 40(11):1959-2004
[16]Schecter M. Morden Methods of Partial Differential Equations. McGraw-Hill international Book Co, 1977
[17]Selberg S, Tesfahun A. Low regularity well-posedness for some nonlinear Dirac equations in one space dimension. Differential Integral Equations, 2010, 23(3/4):265-278
[18]Thirring W E. A soluble relativistic field theory. Ann Phys, 1958, 3:91-112
[19]Zhang Y Q. Global strong solution to a nonlinear Dirac type equation in one dimension. Nonlinear Analysis,2013, 80:150-155
[20]Zhang Y Q, Zhao Q. Global solution to nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.Nonlinear Analysis, 2015, 118:82-96
[2]Bournaveas N, Zouraris G E. Theory and numerical approximations for a nonlinear 1+1 Dirac system.ESAIM Math Model Num Analysis, 2012, 46(4):841-874
[3]Cacciafesta F. Global small solutions to the critical radial Dirac equation with potential. Nonlinear Analysis,2011, 74:6060-6073
[4]Candy T. Global existence for an L2 critical nonlinear Dirac equation in one dimension. Adv Differential Equations, 2011, 16(7/8):643-666
[5]Chen S X. Cauchy problem for semilinear hyperbolic equation of higher order with discontinuous initial data. Acta Math Sci, 1994, 14B(2):121-129
[6]Contreras A, Pelinovsky D, Shimabukuro Y. L2 orbital stability of Dirac solitons in the massive Thirring model. Comm Partial Differential Equations, 2016, 41(2):227-255
[7]Delgado V. Global solution of the Cauchy problem for the(classical)coupled Maxwell-Dirac and other nonlinear Dirac equations. Proc Amer Math Soc, 1978, 69(2):289-296
[8]Escobedo M, Vega L. A semilinear Dirac equation in H~s(R~3)for s> 1. SIAM J Math Anal, 1997, 28(2):338-362
[9]Gross D J, Neveu A. Dynamical symmetry breaking in asymptotically free field theories. Phys Rev D,1974,10:3235-3253
[10]Huh H. Global strong solution to the Thirring model in critical space. J Math Anal Appl, 2011, 381:513-520
[11]Huh H. Global solutions to Gross-Neveu equation. Lett Math Phys, 2013, 103(8):927-931
[12]Huh H, Moon B. Low regularity well-posedness for Gross-Neveu equations. Commun Pure Appl Anal, 2015,14(5):1903-1913
[13]Lax P. Functional Analysis. John Wiely Sons Inc, 2002
[14]Pelinovsky D. Survey on global existence in the nonlinear Dirac equations in one dimension//Ozawa T,Sugimoto M. Harmonic Analysis and Nonlinear Partial Differential Equations. RIMS Kokyuroku Bessatsu,2011:37-50
[15]Sasaki H. Small data scattering for the one-dimensional nonlinear Dirac equation with power nonlinearity.Comm Partial Differential Equations, 2015, 40(11):1959-2004
[16]Schecter M. Morden Methods of Partial Differential Equations. McGraw-Hill international Book Co, 1977
[17]Selberg S, Tesfahun A. Low regularity well-posedness for some nonlinear Dirac equations in one space dimension. Differential Integral Equations, 2010, 23(3/4):265-278
[18]Thirring W E. A soluble relativistic field theory. Ann Phys, 1958, 3:91-112
[19]Zhang Y Q. Global strong solution to a nonlinear Dirac type equation in one dimension. Nonlinear Analysis,2013, 80:150-155
[20]Zhang Y Q, Zhao Q. Global solution to nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.Nonlinear Analysis, 2015, 118:82-96
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